what do you mean by electric flux???
simple. charge distributed on the surface.
how does it vary???
vary... again simple. change the area of the surface.
directly proportional to the surface area? or, directly proportional to the amount of charge on the surface? or some summation of the two? is emf a factor?
it is just like the water tank. how much water can you fill in the water tank. obviously the answer is, depends on the size of the tank. now I hope you can estimate the answer. Goodluck
number of electric field that penetrating the surface
The definition of the electric flux is a sum of how much of an electric field 'flows' through a surface S. Mathematically, the flux \[ \Phi_E = \int_S E \cdot dA \] Have a look at this lecture for a good discussion of what this means intuitively: http://ocw.mit.edu/courses/physics/8-02-electricity-and-magnetism-spring-2002/video-lectures/lecture-3-electric-flux-and-gausss-law/
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